Polymarket-implied volatility vs what happened
The variance a mid-window price implied for the rest of the window was 0.90–1.01 × the variance that then happened, on the 4 markets where it can be measured (Bitcoin 5-minute 1.00, Bitcoin 15-minute 1.01, Ethereum 5-minute 0.95 and Ethereum 15-minute 0.90); the 95% interval contains 1 on 3 of 4. Every figure sits within 10% of 1. This comparison does not depend on the law used to invert the price.
| market | windows kept | variance ratio | first half / second half | implied (level) | realized (level) | Student-t reading |
|---|---|---|---|---|---|---|
| Bitcoin 5-minute | 10,139 (47%) | 1.00 [0.96; 1.04] | 1.01 / 0.98 | 22.6% | 27.8% | 1.29 |
| Bitcoin 15-minute | 4,152 (58%) | 1.01 [0.91; 1.11] | 0.99 / 1.06 | 24.7% | 27.2% | 1.31 |
| Ethereum 5-minute | 10,533 (49%) | 0.95 [0.92; 0.99] | 0.97 / 0.94 | 30.0% | 36.7% | 1.23 |
| Ethereum 15-minute | 3,945 (55%) | 0.90 [0.80; 1.01] | 0.83 / 1.02 | 30.6% | 37.2% | 1.16 |
Method detail: the law decides the sign of the σ gap
Method detail. Read through a normal law, the mid-window implied volatility sits below the trailing realized vol: 0.80–0.94 × across the 12 markets. Read through the fat-tailed Student-t law our model also uses, the same prices give 1.02–1.22 ×. The law you invert through decides the sign of that gap; the variance ratio above does not.
| market | windows kept | normal inversion | Student-t inversion | implied (level) | realized (level) |
|---|---|---|---|---|---|
| Bitcoin 5-minute | 10,139 (47%) | 0.80 [0.79; 0.80] | 1.02 | 22.6% | 27.8% |
| Bitcoin 15-minute | 4,152 (58%) | 0.89 [0.88; 0.90] | 1.15 | 24.7% | 27.2% |
| Bitcoin hourly | 1,138 (63%) | 0.94 [0.93; 0.96] | 1.22 | 25.9% | 27.5% |
| Ethereum 5-minute | 10,533 (49%) | 0.80 [0.80; 0.81] | 1.04 | 30.0% | 36.7% |
| Ethereum 15-minute | 3,945 (55%) | 0.81 [0.81; 0.82] | 1.05 | 30.6% | 37.2% |
| Ethereum hourly | 1,101 (61%) | 0.85 [0.83; 0.86] | 1.10 | 32.5% | 37.5% |
| Solana 5-minute | 10,146 (47%) | 0.82 [0.81; 0.82] | 1.05 | — | — |
| Solana 15-minute | 3,798 (53%) | 0.83 [0.82; 0.84] | 1.07 | — | — |
| Solana hourly | 1,068 (59%) | 0.84 [0.83; 0.85] | 1.08 | — | — |
| XRP 5-minute | 5,242 (24%) | 0.85 [0.84; 0.86] | 1.07 | — | — |
| XRP 15-minute | 2,369 (33%) | 0.83 [0.83; 0.84] | 1.07 | — | — |
| XRP hourly | 744 (41%) | 0.82 [0.80; 0.83] | 1.05 | — | — |
Method
Each night, for every graded window, we take the collector's sample at mid-window (spot, order-book mid, model probability), invert P(Up) = 1 − Φ(K/(σ·√V)) for σ — the formula of the pricer, unchanged — and keep the window only when the mid sits in 15%–45% or 55%–85%: near 50¢ the inversion is unstable, near 0 or 1 it is meaningless. The variance ratio sums σ²·V over the kept windows and divides by the sum of the squared log-moves that followed, same windows, same horizon. Realized volatility is the model's own input (1-minute candles, 60–120 min). Medians with bootstrap 95% CIs; every figure also on two halves of the period.
Questions
What does "implied volatility" mean for an Up or Down market?
The σ such that our pricer, fed the current spot, the price to beat and the time left, returns exactly the market's mid price for Up. It is the movement the price embeds, read in annualized terms — a binary-option implied vol, computed from the pricer that grades our track record.
What is the variance ratio, and why is it shown first?
The variance the mid-window price implied for the remaining half of the window, divided by the variance that then happened on the same windows. It compares a forecast with its outcome on the same horizon, and it reads the same whichever law is used to invert the price — the normal and Student-t readings below depend on that choice.
Why two numbers (normal and Student-t)?
Because the σ you read depends on the law you invert through. Our pricer publishes both a normal and a Student-t probability; the same mid price reads as a smaller σ under the normal law and a larger one under the t law. We show both, as a method detail.
Why mid-window and not the last minute?
One minute before the close most prices sit at 0 or 1: the inversion has nothing to work with, and the last minute is under the TWAP regime. Mid-window keeps about half of the windows and sits far from both.
Is a gap between implied and realized volatility something to act on?
No. It is an observed gap between two measurements, published with its confidence interval and its stability across two halves of the period. Paper results · not financial advice · 18+.
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Paper results · not financial advice · 18+. Data analytics on Polymarket crypto markets.